Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
212 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D281 |
| commutator, socle, cosocle | C22×C281 | C24 |
| Fitting | #126×C281 | C2 |
| prime radical | C2×C22⋊D281 | C22 |
| hypercenter | #126 | D281 |
| hypocenter | C281 | #556 |
| LCS | G ▷ C22×C281 ▷ C281 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22582878 | C2 | semidirect |
| 2. #22582874 | C2 | semidirect |
| 3. #22582874 | C2 | semidirect |
| 4. #22582872 | C2 | semidirect |
| 7. #22582857 | C2 | semidirect |
| 8. #22582856 | C2 | semidirect |
| 9. C4×Dic562 | C2 | semidirect |
| 10. #22582844 | C2 | semidirect |
| 11. #22582844 | C2 | semidirect |
| 13. #22582836 | C2 | semidirect |
| 14. #22582835 | C2 | semidirect |
| 15. #126×C281 | C2 | semidirect |
| 97. C281 | #556 | semidirect |
| 103. #126 | D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582878 | 2 |
| #22582874 | 2 |
| #22582872 | 2 |
| #22582865 | 2 |
| #22582857 | 2 |
| #22582856 | 2 |
| C4×Dic562 | 2 |
| #22582844 | 2 |
| #22582839 | 2 |
| #22582836 | 2 |
| #22582835 | 2 |
| #126×C281 | 2 |
| #556 | 281 |